Question

Find the rate of change of the area of a circle with respect to its radius r when (a) r=3 cm (b) r=4 cm

Answer 1

The correct answer is $8π cm^2 /s$
The area of a circle (A) with radius (r) is given by,
$A=πr^2$
Now, the rate of change of the area with respect to its radius is given by,
$\frac{dA}{dr}=\frac{d}{dr}(πr^2)=2πr$
1. When r=3 cm,
$\frac{dA}{Dr}=2π(3)=6π$
Hence, the area of the circle is changing at the rate of $6π cm^2 /s$ when its radius is 3 cm.
2. When r=4 cm,
$\frac{dA}{dr}=2π(4)=8π$
Hence, the area of the circle is changing at the rate of $8π cm^2 /s$ when its radius is 4 cm.